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The relation between the bottom-hole pressure 

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bodyp_{wf}
 and surface flow rate  
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bodyq
  during the stabilised formation flow (see Inflow Performance Relation (IPR)):

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p_{wf} = p_{wf}(q)

...

[ Vogel IPR @model ] [ Richardson and Shaw IPR @ model ] [ Wiggins IPR @ model ]


Reference

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Gilbert
Gilbert
Gilbert, W.E.: "Flowing and Gas-Lift Well Performance," Drill. and Prod. Prac., API (1954) 126.